All Questions
33
questions
2
votes
1
answer
45
views
Is bayesian updating framework a valid concept?
When I google search for the term, only 6 pages showed up. There is no authoritative paper on this, except https://arxiv.org/abs/1306.6430 which argues for using informatics concepts to generalize a ...
- 21
1
vote
0
answers
25
views
Correctness of product of densities representing parts of information as prior density in Bayes inference
suppose I've got data $X$ from a model driven by parameter $\theta$. Model of data is represented by conditional density (likelihood function)
$$f(x|\theta).$$
Suppose the prior density of $\theta$ is ...
- 81
0
votes
0
answers
69
views
Reparametrizing a Uniform Prior Distribution to Multivariate Standard Normal
Problem Description
I have a posterior distribution
$$
p(\theta\mid y) \propto p(y \mid \theta) p(\theta)
$$
with a uniform prior $p(\theta)= \mathcal{U}([a, b]^n)$, which is bounded. However, for my ...
- 2,236
1
vote
0
answers
37
views
Bayesian Prior definition [closed]
The prior of an inference problem where we try to infer $x$ from observations $y$ is defined as $P(X)$. Often (e.g.) I see another definition where the prior is defined as $P(X|Q)$, what exactly is $Q$...
- 121
1
vote
1
answer
317
views
Prior predictive distribution with an improper prior for a Poisson likelihood
I have recently started exploring some bayesian statistics and I cannot seem to understand something about improper priors. In particular, the set up consists of a Poisson likelihood $ p(X|\theta) = \...
0
votes
0
answers
86
views
Best probability density function to use for the prior of a variance parameter in Bayesian inference
This answer provided some good general advice, but in my specific case I want to create a model of my prior beliefs about the variance of a normally-distributed random variable:
$$x \sim \mathcal{N}(0,...
- 165
4
votes
4
answers
688
views
Is it really worth doing Bayesian Analysis if you have no idea about Priors? [duplicate]
I have heard that if you use uniform priors in Bayesian Analysis, it is the same as doing Frequentist Analysis. If you are creating statistical models and you really have no idea about the prior ...
3
votes
2
answers
623
views
Posterior of one observation transform into posterior of several observations
Suppose $\mu$ has prior distribution $\mathcal{N}(M, A)$ and $x |\mu \sim \mathcal{N}(\mu, 1)$
After one observation, the posterior is $$\mu|x \sim \mathcal{N}(M + B(x-M), B), \tag{1}$$ where $B \...
- 471
1
vote
0
answers
295
views
Postetior from Jeffrey prior of Normal distribtion
Context
I am given a sample from normal distribution $v_i \sim N(\gamma \cdot u_i, \sigma^2)$, $i =1,..., n$.
I need to obtain the posterior distribution using Jeffreys prior for $\gamma$.
My solution
...
- 261
2
votes
0
answers
186
views
When does this prior dominate likelihood?
This is a simple Bayesian inference problem, where we are trying to infer some weight parameter $w$. Our posterior distribution is
$$ P\propto \exp\left(-\frac{1}{\sigma^2} w^Tw\right) \exp\left(-f(w)\...
- 281
1
vote
0
answers
96
views
Determining the Likelihood function from a Uniform Prior
I am trying to find the Bayes factor between two models, which I understand is the ratio of the likelihood functions of each model.
The second model has a uniform prior described by:
$U(A; -a, a) = \...
4
votes
1
answer
28
views
How to jointly model $N$ groups where data in each group is i.i.d. Normal and infer the posterior distribution?
I am given the following data of income scores of individuals from $N$ groups:
$$(\textbf{x}_1, \textbf{x}_2 \ldots \textbf{x}_N),$$
where $$\textbf{x}_j = (x_j^1, x_j^2 \ldots x_j^{N_j}),\quad j = 1, ...
- 151
2
votes
1
answer
6k
views
How to calculate the confidence interval with weighted data?
I've done some search for similar questions, but they're not the same as what I'm trying to get.
Assume that there's a server that handles requests $r$ and returns a set of items $I_{r}$ of random ...
- 21
1
vote
1
answer
94
views
reference request for the impact of priors in bayesian statistics
It is well known that in bayesian statistics, the prior believe can have a large impact on the estimation result. For example if you flip a coin ten times to determine whether it is loaded, a prior $...
- 171
2
votes
2
answers
80
views
Borrowing observations for prior probability in Bayesian Inference
For the purposes of Bayesian Inference, is it assumed that the historical observations used for the prior probability values must be from the exact entity for which you are looking to calculate the ...
- 213